How Special Relativity Makes Magnets Work

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Magnetism seems like a pretty magical phenomenon. Rocks that attract or repel each other at a distance - that's really cool - and electric current in a wire interacts in the same way. What's even more amazing is how it works. We normally think of special relativity as having little bearing on our lives because everything happens at such low speeds that relativistic effects are negligible. But when you consider the large number of charges in a wire and the strength of the electric interaction, you can see that electromagnets function thanks to the special relativistic effect of length contraction. In a frame of reference moving with the charges, there is an electric field that creates a force on the charges. But in the lab frame, there is no electric field so it must be a magnetic field creating the force. Hence we see that a magnetic field is what an electric field becomes when an electrically charged object starts moving.

I was inspired to make this video by Prof. Eric Mazur

Huge thank you to Ralph at the School of Physics, University of Sydney for helping us out with all this magnetic gear. Thanks also to geology for loaning the rocks.

This video was filmed in the studio at the University of New South Wales - thanks to all the staff there for their time and support.

Music: Firefly in a Fairytale, Nathaniel Schroeder, and Love Lost (Instrumental) by Temper Trap licensed from

Views: 1401167
Runtime: 4:19
Comments: 3922

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Author Marcus Tornea ( ago)
Something isn't clear to me here. No, it's not the issue about electrons being length contracted and attracting the positive cat-ion, but look at a permanent magnet. No current runs through a permanent magnet, the magnetic field around a permanent magnet is produced because the electrons, which act like little magnets of their own due to the fact that they spin around their own axis, line up to make a majority magnetic domain. The electrons in the permanent magnet are not length contracted but still do exert an electromagnetic force on charged particles. What is this?

Author Jee Whizz ( ago)
my mind is totally blown!

Author Daniel Skyminer ( ago)
At 1:37, wouldn't the electrons undergo length contraction due to special relativity in the cat's frame of reference (stationary relative to the protons)? Therefore there would be more electrons and the cat would be attracted to the rod, right? What am I missing?

Author TheLegend27 ( ago)
59:9.0999999 nine nine nei nein nein
Hitler says nein
Hitler is evil
i cant rhyme
but this is devil

Author Tarun Chand ( ago)
what about the stationary cat! for the stationary cat should see the electrons contract thus increasing the density of -ve charge. the stationary cat should be attracted! why does it not happen?

Author econogate ( ago)
Everytime people try to define magnetism they always have to refer to gravity and relativity, gee I wonder why? Could it be...naw. We could be piloting crafts with bursts of magnetism but that maybe too much for physicists heads to absorb yet.

Author Vijay Raj ( ago)
OK so that explains magnetism, essentially it's electric field and electric field only.

Now how do you explain a electromagnetic wave? There is no charged particles there right?

Author To Athánatos ( ago)
Well, in my perspective, that cat is utterly repulsive.

Author Tomek ( ago)
How does it relate to amper's law? Current flowing in the same direction in two paralel wires causes them to attract each other. Since moving electrons are causing both wires to be positively charged shouldn't the repel each other???!!!

Author Christian Libertarian ( ago)
Unbelievable. I have learned something. Hasn't happened in years.

Author Sad Man ( ago)
Explanation needed:
If positively charged cat is moving, then even without current there should be some length contraction. (one half of when both the cat and the current are moving).
Does this mean that there is magnetic force even if there is no current as long as the positively charged particle is moving?

Author Yout Tuka ( ago)
I just learned this in physics lecture. Pretty cool!

Also, you can derive the speed of light by setting the electrostatic force equal to magnetic force.

Author Dimitris Davazoglou ( ago)
And how can we explain the mutual attraction between two parallel electron beams, for instance? Now there are no immobile positive ions, just moving negative electrons.

Author Purely Science ( ago)
electro MAG-NETism means NET MAGnitude of electrons.

Author Purely Science ( ago)
that's why MAG-NET means NET MAGnitude of charges.

Author Mazahir Mammadli ( ago)
Name me a textbook that explains this topic even half as simply as Veritasium. Derek, you're a legend!

Author brianjlayman ( ago)
i came here from minute physics :) love both u guys and vsauce

Author SaintDank ( ago)
What if the cat wasn't moving at the same speed as the electrons

Author Infinity 1 ( ago)
100 × pi dislikes

Author Arturo Mena ( ago)

Author aiopqwe ( ago)
I have a question. when the cat is not moving,and the electrons is moving , how come the cat doesnt see the electrons more dense,and feel the attraction? why does it work only the other way around ?

Author Arne ( ago)
Fantastic explanation!

Author John Doe ( ago)
Everyday magnetism is generated by quantum mechanics, and in particular quantum statistics. Everyday magnets are ferromagnetic, and ferromagnets arise due to the coupling between neighboring molecules/atoms/particles' net magnetic moment due to intrinsic spin. This coupling results in energy costs and savings when the relative spins are aligned or non aligned, producing a material that will tend to be all in the same spin state, resulting in a net magnetic moment.

Author Matthew Barnett ( ago)
you guys have a great sense of humour.

Author takeitindballs ( ago)
This whole explanation is so full of holes that it's a joke.  For starters, when the charged cat was introduced and the electrons were shown moving, why didn't you apply the same "logic" and say that the distance between the electrons shrunk and the protons stretched and therefore created a negative push?  This is without even going into the notion some "force" thingy exerting onto external objects.  How is that "force" applied PHYSICALLY?  Magic?  Some void-jumping ghost?  The Rope Hypothesis is a far better explanation.

Author RESTLINXXX ( ago)
hm ,now if we just had just two moving charges and we were travelling with one of the two there should be no magnetic force but we know there is .How relativity would make this simplest case to work?

Author TheSkepticSniper 001 ( ago)
awesome vid subscribed!

Author lighthablunt ( ago)
There is something wrong when it's said that even with current flowing through the wire the kitty would still not be repelled/attracted. That might be true (i'm not a physician) but it needs a better explanation because there is a contradiction.

Author JamesOscar ( ago)
Einstein? LOL
The Theory of Relativity is a beggar wrapped in purple whom ignorant people take for a king.

Author Harjit Sajjan ( ago)
dereck has a pretty thick 5:59:59.9999999999999 hour shadow

Author Rahul Sharma ( ago)
What will be the effect when we replace the cat-ion with a neutral piece of iron which is NOT moving, initially... In stationary frame, the 'magnetic field' will attract iron... Right...??

Now lets say the piece of iron begins to move just like the example in the video (at the same velocity as the negative charges)... Then what will happen...?? How should the piece of iron behave in its own moving frame of reference...??

Author iridium137 ( ago)
Under this explanation, a positively-charged cat moving at half the drift velocity of the electrons in the wire should experience no electrostatic force. (Because relative to the cat, the velocity of the protons and electrons are opposite but equal in magnitude, so length contraction is the same.) But I'm pretty sure the cat is still repelled.

Author ron9ist ( ago)
but whatif there's no electron n proton but only interaction of two masses due to mass difference??

Author Kathleen Mitchell ( ago)
Veritasium : Does this also explain the difference between static and kinetic friction? If there are gaps that are the same size as you when you are not moving you would settle in to them, but then when you start moving the gaps collapse slightly and you can skate over the top of them...?

Author Saeed Baig ( ago)
1:56- Y would the seperation of the positive charges be contracted?
I thought special relativity stated that objects contract in the direction of motion. So if each individual positive charge contracts in the same direction (as they are all moving in the same direction), wouldn't the overall space between them actually increase, resulting in LOWER positive density?

Author Saeed Baig ( ago)
Misleading title. He didn't really explain how magnets work in reference to special relativity. He explained how (like) charges travelling in opposite directions are repelled with reference to special relativity.

Author Ge Zhi ( ago)
wait a sec, why is the cat moving????

Author Red Wolf ( ago)
Aaaaaaaand it's a loop of videos you can never get out of if you follow their instructions. Take that, Vsauce3!

Author bloodbred ( ago)
So electromagnets work because of an electro-quantum level time/space distortion relative to the position of a macro-event?
As difficult as it is to admit, I'm actually starting to understand what was pissing off Shaggy 2 Dope.

Author Thomas Parker ( ago)
Dear +Veritasium and +minutephysics I realise this was a long time ago but it seems that many of the viewers here are still unsure of why your explanation does not rule out attraction of the positively charged cat to the wire when there is a current running through it. It seems rational to assume that space dilation would occur for the moving electrons relative to the stationary cat, and therefore the higher density of negative charge would attract the cat towards it. Some in the comments have explained the lack of attraction by using the concept of a flow of positive charge or transistor like "holes" in the opposite direction to the electrons instead of the stationary positive charge as shown in the video. However, this explanation is disputed by others who say that this model is not correct for a very conductive material like copper, as the electrons movements are not discrete hops like in transistors. If you see this could you guys confirm what is going on and enlighten the confused comment section with your superior skill and knowledge :). Thanks and loving the videos, I've learned so much from you both.

Author carl rimaitis ( ago)
what would happen if we cut the wire and connected each end to a permanent magnet?

Author Fun Living ( ago)

Author dirac17 ( ago)
This is one of the best videos on YouTube.

Author radioactivated ( ago)
what happens when the cat-ion isn't moving, but there is a current in the wire?

Author DB ( ago)
You have highlighted a weakness of the theory of relativity in the first few seconds with the analogy of the person standing on the cliff compared to the person falling. You claim time is slower for the person falling because he is travelling faster than the stationary person. However in true relativity the stationary person is travelling faster from the perspective of the falling person and therefore time is going slower for the stationary person even though he has done nothing. In other words, as a stationary observer you can make your claim, but if you are travelling with the falling person, time is slower for the stationary person who is moving away from you at the speed at which you are falling. Any attempt to explain how magnets work with such a view of relativity is on shaky ground.

Author Wayne Bogue ( ago)
where on a flat disk you stupid f*** not a globe we've only drilled a 12 f****** mouth hole and nothing has changed in that 12 f****** miles from what's on the cross to 12 f****** miles

Author dlwatib ( ago)
I have a really hard time wrapping my head around the idea that an electric field in one frame of reference can be a magnetic field in another frame of reference. If that's "true" for the relativistic concept of truth, then they must in actuality be the same field. If that's true, then why not work with the real thing instead of these complicated chameleon-like substitutes?

Author dlwatib ( ago)
That explains why it's so hard to parallel park. Relativity makes your car bigger when you slow down. :^)

Author Didier Khwartz ( ago)
Clear And Efficient Description of this Theory; Thanks :) 👍

Author bjnartowt ( ago)
Earlier in a semester when I was teaching physics, I said that special relativity implied magnetism, but I declined to furnish a satisfactory explanation out of fear that the discussion could become complicated.

Well, as it turns out, I was too stupid to see that it actually isn't complicated : )

Thanks for this video.

Author Moon Majumdar ( ago)
+Veritasium then why do magnetic needles deflect if kept beside a current carrying wire?

Author Branko Badrljica ( ago)
So why wasn't the static cat attracted by electron flow by the same principle ?

Electron density should slightly increase by the same principle as it was explained later for movin photons.

Author Kjara Plaku ( ago)
can you do something about electromangnetic waves in medicine

Author UnTiedMusicStudio ( ago)
Special Relativity was actually CREATED to describe exactly these effects: charges moving in wires!

Author Jeeshant Choudhary ( ago)
You can say in electron frame ,electron are at rest and proton are moving and the rest as you explained

Author Jeeshant Choudhary ( ago)
Plz explain

Author Jeeshant Choudhary ( ago)
But in my frame electron are moving thus creating a greater density of electron,gaining more negative so the cat should be attracted

Author nightmare5479 ( ago)
Hi guys, Sorry for such a naive question but length contraction or not the density of negative and positive charges across the length of the wire are still the same, Isn't it? If so then how does the cat-ion still get repelled?

Author Reiner Surya ( ago)
can i make an electromagnet from Calcium?, if yes how much electric current does it need?

Author Ben Griffin ( ago)
This explanation doesn't work. Special relativity says there is no preferred inertial frame of reference. So when the Cation is not moving with respect to the wire ( and it's positive charges) the moving negative charges should appear closer together and the Cation should be attracted to the wire.
That is not the case though. The Cation is only attracted to the wire when it is moving with respect to the wire (and it's positive charges) in a direction antiparalell (or with an antiparalell component).

Author Albert Brown ( ago)
lol @ "the 'wizadry' of permanent magnets"

Author Shay Lempert ( ago)
so magnetism is a semi-force?

Author The Porcupine ( ago)
this channel is amazing. Im in my first year of bio engineering a very heavy science course and I still learned a thing or 2 from this channel.

Author Yaman Nidhi ( ago)
But when the cat is not moving and the current is passed, even then with respect to her the electrons are moving and protons aren't. Then according to SR, there should be length contraction in electron-space and expansion in proton-space, thus making the wire, with respect to any stationary outside observer... negatively charged? That means the positive charge should be attracted towards the wire? Am I wrong?

Author Seanisawesome000 ( ago)
Magnets are awesome!

Author CJ Futch ( ago)
But... The electrons are moving relative to the stationary observer, so they should be subject to length contraction, so the wire should have a net negative charge to the stationary observer.... Right? So the cat should be attracted if it wasn't moving, feel no force if it was moving half the speed of the electrons, and should be repelled if it was moving at the same speed of the electrons.... Right? I'm confused at why this wasn't explained.

P.S. I'm writing a paper on magnetism, so I'd genuinely like to know the answer.

Author Gummy Bugz ( ago)
cat ion
I just got the pun, ah Dereck you sly bastard

Author El Dacnomaniac ( ago)
The way the information in this video is demonstrated is making it way harder for me to follow along

Author Lukáš Fireš ( ago)
0:52 Why is the length contraction not applied to electrons moving in wire's frame of reference?
1:32 Yes, the density of positive (protons? holes?) and negative (electrons) must be the same, but still, why is the 'stationary distance' of those moving electrons different from distance between protons?

It can hardly be any other way, so, forming a closed loop, nothing changes from wire's perspective. When we look at closed loop from cation's perspective, positive charges are moving, negative charges in one part of wire are stationary and negative charges in the other part are nearly double the speed.

Ok, I don't know what happens at the curves, but I can make the straight lines as long as I want, so, the density of those two parts have to cancel each out - it does not matter what happens at the curves. There is positive charge in the part where electrons are stationary and negative charge where they are moving, because the moving electrons are denser compared to the stationary ones and the density of protons is somewhere inbetween (according to relative speed - we are only translating the wire's frame of reference where the density is same for all of them).

...but again, why is the density the same for all electrons and protons in wire's frame of reference despite the fact that moving electrons *should be* denser? What keeps the distance the same between no-power state (electrons not moving) and powered state (electrons moving)?

Author Mariusz Kreft ( ago)
Are you sure about speed of electrons in copper ? 0,00000001% ? It's about 2200 km per second

Author Patrick Notstar ( ago)
So does that mean a negatively charged cat standing still would be repelled

Author Gagan Narang ( ago)
but the compass wasn't moving like the cat-ion was why it gets deflected?!

Author Abigail Park ( ago)
Temper trap at the end <3

Author Robert Bielik ( ago)
And if the wire is a closed loop (with current induced), how is the charge imbalance handled ? From the wires perspective, there would now be a depletion of electrons due to length contraction. Where do the extra electrons come from ? And from the "cats" perpective there would be a depletion of positive charges due to length contraction. This is nonsense and a clear indicator that the explanation is bunk.

Author Veine Haglund ( ago)
So there's this other thing I've been wondering for some time, I hope there are some physicists out there who can help me:

If magnetic fields are basically electric fields viewed from a different frame of reference, how should I interpret the idea of light being a self-propagating electromagnetic wave/particle (where the electric field is feeding a magnetic field and vice versa)? Is it just from my perspective that it changes appearance, or is there some sort of duality involved in this energy transmission?

Or is it rather my perspective of the source of the wave (for example an oscillating charge), and my position/movement relative to the source?

Author BitMiller ( ago)
That is a cute animation, dear Derek and Henry. But I would be sooo happy, if You could make us an animation showing the WHOLE AND CLOSED electric circuit! If positive charges would closen to each other to be more crowded, a gap would form on the circuit somewhere, or on multiple locations, no? To fill it up, where would the other positive charges come from? From deep space, hidden quantum world? :) But this is said only for the point of view of the cat with the positively charged head of course. Everybody else resting relative to the wire forming a CLOSED CIRCUIT would experience unchanged and still positive charges... Oh man... Are You guys serious?...

Author Roger Nevez ( ago)
best explanation ever

Author Orion Burch ( ago)
WHAT!!??! That is so cool.

Author mdhussam ( ago)
Now I understood what Einstein relativity actually want us to believe ??

Author Paul Smith ( ago)
Wow...that is all

Author Tomi Lee TRNíK ( ago)
indeed, this experiment verified theory?
I can not believe it. (

Because I have not yet thought
the EM field created by
electron jumps from atom to atom,

so that the electron is initially at about the speed of 0 km/h with respect to the hub (cat) outside the wire,
and it is simply jumps 150 000 km/h,
and is braked to 0 km/h,

and in this it creates around the EM field ...

Author hobyrne ( ago)
On my fourth viewing of this video, I realized I was looking at... a cat-ion.

Author Eby Zoid ( ago)
Thats perfectly illogical, by ignoring the mechanics of magnetic fields, which are not electric fields xD ... magnetic forcefields act vectorial differently upon electric fields than upon magnetic fields ...

Author SuperMagnetizer ( ago)
This video is extremely misleading.  When the cat shared the same reference frame as the unshaven dude (UD), the electron current was started up and NO length contraction was shown. Yet when the cat was then given the same velocity as the electron current, the relatively moving proton current WAS shrunken AND the electron current (now stationary relative to the cat) was EXPANDED in order to explain the repulsion of the cat from the wire.  This makes no sense.

Author SuperMagnetizer ( ago)
"Special Relativity is the fact that in our Universe length and time aren't absolute."  WRONG!  Special Relativity is a theory, not a fact.

Author Jannuel Lauro Dizon ( ago)

Author Jordan L ( ago)
Funny you should say that things "slim down" when moving. I definitely feel that runners are slimmer than the lazy people spending all day sitting.

Author Shubham Jhariya ( ago)
I want to ask when charge particles are taken individualy means only electron and proton are in motion in evacuated space. so there is relatively applicable.

Author Yuvan Seth ( ago)
Cant electromagnetism be explained by :-
In a conductor, the free electrons move in random directions, hence cancelling out their overall magnetism. But as soon as current is allowed to pass, the free electrons move in a specific directions, thus their magnetism adds up and creates an overall magnet?

Author Ivan Krylov ( ago)
You need to make a full-on Bill Nye type of series but with college-level material

Author Marco Discendenti ( ago)
So you are assuming
(1) Coulomb electrostatic law applies in any reference frame
(2) SR applies
then we can prove also Lorentz magnetic force must apply?

Author Valentin Tihomirov ( ago)
Will wire contract when we make a transition into the cat's frame of ref? They should, according to Einsteins' special relativity. But how does the same amount of expanded electrons fit into the contracted loop?

Author Curiosity Guy ( ago)
So this means that if You increase speed of electrons, the magnetic field is stronger, that is voltage controls strength of magnetic field

Author Balaji Panneer ( ago)
how the rotating magnetic field(concentric circles) is created? pls explain clearly

Author Giampiero Baggi ( ago)
Congratulatuons, you have succesfully created an infinite loop of video links!

Author JaSamZaljubljen ( ago)
You are a genious,everyone else would give you simplistic unlogical textbox refferences or explanations,thank you! :D

Author Nick Evans bodybuilding ( ago)

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